\begin{table}

\caption{Registration and Voting by Treatment Arm (By Previous Registration)) \label{maincoefftable_byreg}}
\centering
\begin{tabular}[t]{lcccc}
\toprule
  & Voter Registration & Turnout & (Re)Registration & Turnout \\
\midrule
Information-Only Mail (T1) & \num{0.0025} & \num{0.0015} & \num{0.0051} & \num{0.0048}\\
 & (\num{0.0027}) & (\num{0.0011}) & (\num{0.0055}) & (\num{0.0101})\\
Research-Informed Mail (T2) & \num{0.0068}* & \num{0.0038}* & \num{0.0127}* & \num{0.0094}\\
 & (\num{0.0028}) & (\num{0.0013}) & (\num{0.0057}) & (\num{0.0101})\\
\midrule
Difference: T2-T1 & 0.0043 & 0.0023 & 0.0075 & 0.0045\\
 & (0.0030) & (0.0015) & (0.0061) & (0.0106)\\
Num.Obs. & \num{15760} & \num{15760} & \num{8008} & \num{8008}\\
Control Mean & 0.018 & 0.0027 & 0.0405 & 0.1614\\
\bottomrule
\multicolumn{5}{l}{\rule{0pt}{1em}* p $<$ 0.05}\\
\end{tabular}
\end{table}
